Subgroups — C₁₃×#61959 #15748298

Order 3328.

2178 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3310	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3264	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3038	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
21	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#553	—	2	1	no	—
25	C₁₃×#552	—	2	1	no	—
26	C₁₃×#552	C₂²	1	2	yes	complemented
27	C₁₃×#551	—	2	2	no	—
28	C₁₃×#550	—	2	1	no	—
29	C₁₃×#550	C₂²	1	2	yes	complemented
30	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#546	C₂²	1	2	yes	complemented
32	D₄²×C₁₃	—	2	1	no	—
33	D₄²×C₁₃	—	2	2	no	—
34	D₄²×C₁₃	C₂²	1	4	yes	—
35	D₄²×C₁₃	C₂²	1	2	yes	complemented
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#535	—	2	2	no	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
43	C₁₃×#529	—	2	2	no	—
44	C₁₃×#529	C₂²	1	2	yes	complemented
45	C₁₃×#525	—	2	1	no	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#117	—	2	1	no	—
50	C₁₃×#496	C₂²	1	4	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	complemented
52	C₁₃×#490	C₂²	1	4	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#482	C₂²	1	4	yes	complemented
55	C₁₃×#480	C₂²	1	2	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#476	C₂²	1	2	yes	complemented
58	C₁₃×#475	C₂²	1	2	yes	complemented
59	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#469	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	complemented
63	C₁₃×#465	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#461	C₂²	1	2	yes	complemented
66	C₁₃×#460	C₂²	1	4	yes	complemented
67	C₁₃×#460	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#460	C₂²	1	2	yes	complemented
70	C₁₃×#459	C₂²	1	4	yes	complemented
71	C₁₃×#459	C₂²	1	2	yes	complemented
72	C₁₃×#459	C₂²	1	2	yes	complemented
73	C₁₃×#459	C₂²	1	2	yes	complemented
74	C₁₃×#459	C₂²	1	2	yes	complemented
75	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#450	C₂²	1	4	yes	complemented
78	C₁₃×#450	C₂²	1	4	yes	complemented
79	C₁₃×#449	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	2	yes	complemented
81	C₁₃×#447	C₂²	1	4	yes	complemented
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₁₃×#442	C₂²	1	4	yes	complemented
84	C₁₃×#440	C₂²	1	4	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
86	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
87	C₁₃×#436	C₂²	1	2	yes	complemented
88	C₁₃×#435	C₂²	1	4	yes	complemented
89	C₁₃×#432	C₂²	1	2	yes	complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#418	C₂²	1	4	yes	complemented
94	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
95	C₁₃×H(5,𝔽₂)	—	4	8	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃	—	2	4	no	—
102	C₂²×D₄×C₁₃	—	2	2	no	—
103	C₂²×D₄×C₁₃	—	2	1	no	—
104	C₂²×D₄×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	—	2	1	no	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
110	C₂³×C₄×C₁₃	—	2	1	no	—
111	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×D₈	—	4	4	no	—
116	C₂×C₁₃×D₈	C₂³	1	2	yes	—
117	C₂×C₁₃×D₈	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	2	yes	—
119	C₂×C₁₃×D₈	C₂³	1	4	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₃×#127	—	2	1	no	—
126	C₁₃×#127	—	2	1	no	—
127	C₁₃×#127	—	2	2	no	—
128	C₁₃×#127	—	2	2	no	—
129	C₁₃×#127	C₂³	1	2	yes	—
130	C₁₃×#127	C₂³	1	1	yes	characteristic
131	C₁₃×#127	C₂³	1	2	yes	—
132	C₁₃×#127	C₂³	1	4	yes	—
133	C₁₃×#126	—	2	2	no	—
134	C₁₃×#126	—	2	2	no	—
135	C₁₃×#126	—	2	2	no	—
136	C₁₃×#125	—	2	2	no	—
137	C₁₃×#125	—	2	1	no	—
138	C₁₃×#125	C₂³	1	2	yes	—
139	C₁₃×#124	—	2	2	no	—
140	C₁₃×#124	—	2	1	no	—
141	C₁₃×#124	—	2	2	no	—
142	C₁₃×#124	C₂³	1	2	yes	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	—	2	4	no	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	C₂³	1	2	yes	—
163	C₁₃×#121	C₂³	1	2	yes	—
164	C₁₃×#121	C₂³	1	4	yes	—
165	C₁₃×#120	—	2	2	no	—
166	C₁₃×#120	—	2	4	no	—
167	C₁₃×#120	—	2	4	no	—
168	C₁₃×#120	—	2	4	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	D₄	1	2	yes	—
182	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	4	yes	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	2	yes	—
191	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	—	2	2	no	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	D₄	1	1	yes	characteristic
199	C₁₃×#117	D₄	1	2	yes	—
200	C₁₃×#117	C₂³	1	2	yes	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₄²×C₁₃	—	2	2	no	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	2	yes	—
211	C₁₃×#106	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₃×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₁₃	C₂³	1	2	yes	—
231	#61959	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	1	no	—
233	C₂⁴×C₁₃	—	2	4	no	—
234	C₂⁴×C₁₃	—	2	2	no	—
235	C₁₃×#41	—	2	4	no	—
236	C₁₃×#41	—	2	4	no	—
237	C₁₃×#41	—	4	2	no	—
238	C₁₃×#41	—	4	8	no	—
239	C₁₃×#41	—	4	8	no	—
240	C₁₃×#41	—	4	4	no	—
241	C₂×Q₈×C₁₃	—	2	1	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	4	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	4	1	no	—
262	C₂×D₄×C₁₃	—	4	2	no	—
263	C₂×D₄×C₁₃	—	4	4	no	—
264	C₂×D₄×C₁₃	—	4	2	no	—
265	C₂×D₄×C₁₃	—	4	4	no	—
266	C₂×D₄×C₁₃	—	4	8	no	—
267	C₂×D₄×C₁₃	—	4	16	no	—
268	C₂×D₄×C₁₃	—	4	8	no	—
269	C₂×D₄×C₁₃	—	4	4	no	—
270	C₂×D₄×C₁₃	—	8	2	no	—
271	C₂×D₄×C₁₃	—	8	4	no	—
272	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
275	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	—	2	1	no	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	1	no	—
283	C₂²×C₄×C₁₃	—	2	1	no	—
284	C₂²×C₄×C₁₃	—	2	4	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	4	4	no	—
288	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₁₃×SD₁₆	—	4	4	no	—
295	C₁₃×SD₁₆	—	4	4	no	—
296	C₁₃×SD₁₆	—	4	4	no	—
297	C₁₃×D₈	—	2	8	no	—
298	C₁₃×D₈	—	2	4	no	—
299	C₁₃×D₈	—	4	4	no	—
300	C₁₃×D₈	—	4	2	no	—
301	C₁₃×M₁₆	—	4	4	no	—
302	C₂×C₈×C₁₃	—	4	2	no	—
303	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
304	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
305	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	2	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
317	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
319	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	1	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	1	no	—
332	C₁₃×C₂²⋊C₄	—	2	1	no	—
333	C₁₃×C₂²⋊C₄	—	2	1	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	4	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
341	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
342	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	C₂×D₄	1	2	yes	—
347	C₄²×C₁₃	C₂×D₄	1	2	yes	—
348	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₄²×C₁₃	C₂⁴	1	2	yes	—
352	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
353	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3397	C₂×C₁₃	1	2	yes	complemented
356	#3366	C₂×C₁₃	1	2	yes	complemented
357	#3325	C₂×C₁₃	1	2	yes	complemented
358	#3310	C₂×C₁₃	1	4	yes	complemented
359	#3272	C₂×C₁₃	1	2	yes	complemented
360	#3264	C₂×C₁₃	1	4	yes	complemented
361	#3251	C₂×C₁₃	1	2	yes	complemented
362	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3217	C₂×C₁₃	1	2	yes	complemented
364	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3115	C₂×C₁₃	1	2	yes	complemented
366	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
367	#3038	C₂×C₁₃	1	2	yes	complemented
368	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
370	C₂³×C₁₃	—	2	1	no	—
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	4	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	4	2	no	—
375	C₂³×C₁₃	—	4	8	no	—
376	C₂³×C₁₃	—	4	2	no	—
377	C₂³×C₁₃	—	4	4	no	—
378	C₂³×C₁₃	—	8	1	no	—
379	C₂³×C₁₃	—	8	2	no	—
380	C₂³×C₁₃	—	8	4	no	—
381	C₂³×C₁₃	—	8	2	no	—
382	C₂³×C₁₃	—	8	4	no	—
383	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	Q₈×C₁₃	—	2	2	no	—
386	Q₈×C₁₃	—	2	2	no	—
387	Q₈×C₁₃	—	2	2	no	—
388	Q₈×C₁₃	—	4	2	no	—
389	Q₈×C₁₃	—	8	1	no	—
390	D₄×C₁₃	—	2	4	no	—
391	D₄×C₁₃	—	2	2	no	—
392	D₄×C₁₃	—	2	4	no	—
393	D₄×C₁₃	—	2	2	no	—
394	D₄×C₁₃	—	2	1	no	—
395	D₄×C₁₃	—	2	1	no	—
396	D₄×C₁₃	—	2	1	no	—
397	D₄×C₁₃	—	2	2	no	—
398	D₄×C₁₃	—	2	4	no	—
399	D₄×C₁₃	—	4	2	no	—
400	D₄×C₁₃	—	4	8	no	—
401	D₄×C₁₃	—	4	2	no	—
402	D₄×C₁₃	—	4	4	no	—
403	D₄×C₁₃	—	4	4	no	—
404	D₄×C₁₃	—	4	8	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	2	no	—
407	D₄×C₁₃	—	4	4	no	—
408	D₄×C₁₃	—	4	4	no	—
409	D₄×C₁₃	—	8	4	no	—
410	D₄×C₁₃	—	8	2	no	—
411	D₄×C₁₃	—	8	4	no	—
412	D₄×C₁₃	—	8	2	no	—
413	D₄×C₁₃	—	8	2	no	—
414	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
415	C₂×C₄×C₁₃	—	2	4	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	4	2	no	—
426	C₂×C₄×C₁₃	—	4	1	no	—
427	C₂×C₄×C₁₃	—	4	4	no	—
428	C₂×C₄×C₁₃	—	4	8	no	—
429	C₂×C₄×C₁₃	—	4	2	no	—
430	C₂×C₄×C₁₃	—	4	2	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	4	2	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	4	4	no	—
435	C₂×C₄×C₁₃	—	8	2	no	—
436	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
437	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
446	C₈×C₁₃	—	2	4	no	—
447	C₈×C₁₃	—	2	2	no	—
448	C₈×C₁₃	—	2	2	no	—
449	C₂×H(5,𝔽₂)	—	2	1	no	—
450	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
451	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
452	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#553	—	2	1	no	—
456	#552	—	2	1	no	—
457	#552	C₂²×C₁₃	1	2	yes	complemented
458	#551	—	2	2	no	—
459	#550	—	2	1	no	—
460	#550	C₂²×C₁₃	1	2	yes	complemented
461	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#546	C₂²×C₁₃	1	2	yes	complemented
463	D₄²	—	2	1	no	—
464	D₄²	—	2	2	no	—
465	D₄²	C₂²×C₁₃	1	4	yes	—
466	D₄²	C₂²×C₁₃	1	2	yes	complemented
467	#535	—	2	1	no	—
468	#535	—	2	2	no	—
469	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	#532	C₂²×C₁₃	1	1	yes	characteristic
471	#532	C₂²×C₁₃	1	2	yes	complemented
472	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
474	#529	—	2	2	no	—
475	#529	C₂²×C₁₃	1	2	yes	complemented
476	#525	—	2	1	no	—
477	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
478	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
479	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	C₂×#117	—	2	1	no	—
481	#496	C₂²×C₁₃	1	4	yes	complemented
482	#492	C₂²×C₁₃	1	2	yes	complemented
483	#490	C₂²×C₁₃	1	4	yes	complemented
484	#486	C₂²×C₁₃	1	2	yes	complemented
485	#482	C₂²×C₁₃	1	4	yes	complemented
486	#480	C₂²×C₁₃	1	2	yes	complemented
487	#478	C₂²×C₁₃	1	4	yes	complemented
488	#476	C₂²×C₁₃	1	2	yes	complemented
489	#475	C₂²×C₁₃	1	2	yes	complemented
490	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#469	C₂²×C₁₃	1	4	yes	complemented
493	#468	C₂²×C₁₃	1	4	yes	complemented
494	#465	C₂²×C₁₃	1	4	yes	complemented
495	#463	C₂²×C₁₃	1	4	yes	complemented
496	#461	C₂²×C₁₃	1	2	yes	complemented
497	#460	C₂²×C₁₃	1	2	yes	complemented
498	#460	C₂²×C₁₃	1	4	yes	complemented
499	#460	C₂²×C₁₃	1	2	yes	complemented
500	#460	C₂²×C₁₃	1	2	yes	complemented
501	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
503	#459	C₂²×C₁₃	1	4	yes	complemented
504	#459	C₂²×C₁₃	1	2	yes	complemented
505	#459	C₂²×C₁₃	1	2	yes	complemented
506	#459	C₂²×C₁₃	1	2	yes	complemented
507	#459	C₂²×C₁₃	1	2	yes	complemented
508	#450	C₂²×C₁₃	1	4	yes	complemented
509	#450	C₂²×C₁₃	1	4	yes	complemented
510	#449	C₂²×C₁₃	1	4	yes	complemented
511	#447	C₂²×C₁₃	1	2	yes	complemented
512	#447	C₂²×C₁₃	1	4	yes	complemented
513	#446	C₂²×C₁₃	1	2	yes	complemented
514	#442	C₂²×C₁₃	1	4	yes	complemented
515	#440	C₂²×C₁₃	1	4	yes	complemented
516	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
517	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
518	#436	C₂²×C₁₃	1	2	yes	complemented
519	#435	C₂²×C₁₃	1	4	yes	complemented
520	#432	C₂²×C₁₃	1	2	yes	complemented
521	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
522	#423	C₂²×C₁₃	1	2	yes	complemented
523	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	#418	C₂²×C₁₃	1	4	yes	complemented
525	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
526	C₂²×C₁₃	—	2	1	no	—
527	C₂²×C₁₃	—	2	1	no	—
528	C₂²×C₁₃	—	2	2	no	—
529	C₂²×C₁₃	—	2	2	no	—
530	C₂²×C₁₃	—	2	2	no	—
531	C₂²×C₁₃	—	2	2	no	—
532	C₂²×C₁₃	—	4	1	no	—
533	C₂²×C₁₃	—	4	1	no	—
534	C₂²×C₁₃	—	4	4	no	—
535	C₂²×C₁₃	—	4	2	no	—
536	C₂²×C₁₃	—	4	1	no	—
537	C₂²×C₁₃	—	4	1	no	—
538	C₂²×C₁₃	—	4	4	no	—
539	C₂²×C₁₃	—	4	2	no	—
540	C₂²×C₁₃	—	4	1	no	—
541	C₂²×C₁₃	—	4	4	no	—
542	C₂²×C₁₃	—	4	2	no	—
543	C₂²×C₁₃	—	8	4	no	—
544	C₂²×C₁₃	—	16	4	no	—
545	C₂²×C₁₃	—	16	8	no	—
546	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
547	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₁₃	—	2	1	no	—
549	C₄×C₁₃	—	2	2	no	—
550	C₄×C₁₃	—	2	1	no	—
551	C₄×C₁₃	—	2	2	no	—
552	C₄×C₁₃	—	2	1	no	—
553	C₄×C₁₃	—	2	2	no	—
554	C₄×C₁₃	—	4	2	no	—
555	C₄×C₁₃	—	4	2	no	—
556	C₄×C₁₃	—	4	1	no	—
557	C₄×C₁₃	—	4	1	no	—
558	C₄×C₁₃	—	4	2	no	—
559	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
560	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
561	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₄×C₁₃	#585	1	1	yes	characteristic
563	H(5,𝔽₂)	—	4	8	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
568	C₂×#41	C₂³×C₁₃	1	2	yes	—
569	C₂²×D₄	—	2	4	no	—
570	C₂²×D₄	—	2	2	no	—
571	C₂²×D₄	—	2	1	no	—
572	C₂²×D₄	—	2	2	no	—
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
577	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
578	C₂³×C₄	—	2	1	no	—
579	AGL(1,ℤ/8)	—	4	8	no	—
580	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
583	C₂×D₈	—	4	4	no	—
584	C₂×D₈	C₂³×C₁₃	1	4	yes	—
585	C₂×D₈	C₂³×C₁₃	1	2	yes	—
586	C₂×D₈	C₂³×C₁₃	1	4	yes	—
587	C₂×D₈	C₂³×C₁₃	1	2	yes	—
588	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
589	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	#127	—	2	1	no	—
594	#127	—	2	1	no	—
595	#127	—	2	2	no	—
596	#127	—	2	2	no	—
597	#127	C₂³×C₁₃	1	2	yes	—
598	#127	C₂³×C₁₃	1	2	yes	—
599	#127	C₂³×C₁₃	1	1	yes	characteristic
600	#127	C₂³×C₁₃	1	4	yes	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	—	2	1	no	—
606	#125	C₂³×C₁₃	1	2	yes	—
607	#124	—	2	2	no	—
608	#124	—	2	1	no	—
609	#124	—	2	2	no	—
610	#124	C₂³×C₁₃	1	2	yes	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	C₂²⋊Q₈	—	2	1	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
620	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
621	#121	—	2	1	no	—
622	#121	—	2	1	no	—
623	#121	—	2	1	no	—
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	4	no	—
627	#121	—	2	4	no	—
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	C₂³×C₁₃	1	2	yes	—
631	#121	C₂³×C₁₃	1	2	yes	—
632	#121	C₂³×C₁₃	1	4	yes	—
633	#120	—	2	2	no	—
634	#120	—	2	4	no	—
635	#120	—	2	4	no	—
636	#120	—	2	4	no	—
637	C₄×Q₈	—	2	1	no	—
638	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
639	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
640	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
641	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	D₄×C₁₃	1	2	yes	—
650	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₁₃	1	2	yes	—
656	C₄×D₄	C₂³×C₁₃	1	2	yes	—
657	C₄×D₄	C₂³×C₁₃	1	4	yes	—
658	C₄×D₄	C₂³×C₁₃	1	2	yes	—
659	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
660	#117	—	2	1	no	—
661	#117	—	2	1	no	—
662	#117	—	2	1	no	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	—	2	2	no	—
666	#117	D₄×C₁₃	1	1	yes	characteristic
667	#117	D₄×C₁₃	1	2	yes	—
668	#117	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄⋊C₄	—	2	1	no	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₄²	—	2	2	no	—
675	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
677	#107	C₂³×C₁₃	1	2	yes	—
678	#107	C₂³×C₁₃	1	2	yes	—
679	#106	C₂³×C₁₃	1	4	yes	—
680	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
681	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
682	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
683	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
684	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
685	#103	C₂³×C₁₃	1	4	yes	—
686	#102	C₂³×C₁₃	1	4	yes	—
687	#102	C₂³×C₁₃	1	4	yes	—
688	#102	C₂³×C₁₃	1	2	yes	—
689	#102	C₂³×C₁₃	1	4	yes	—
690	#102	C₂³×C₁₃	1	4	yes	—
691	#102	C₂³×C₁₃	1	2	yes	—
692	#102	C₂³×C₁₃	1	2	yes	—
693	#102	C₂³×C₁₃	1	2	yes	—
694	#102	C₂³×C₁₃	1	4	yes	—
695	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
696	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
697	#97	C₂³×C₁₃	1	4	yes	—
698	C₄×C₈	C₂³×C₁₃	1	2	yes	—
699	C₂×C₁₃	—	2	2	no	—
700	C₂×C₁₃	—	4	2	no	—
701	C₂×C₁₃	—	4	2	no	—
702	C₂×C₁₃	—	8	1	no	—
703	C₂×C₁₃	—	8	4	no	—
704	C₂×C₁₃	—	8	2	no	—
705	C₂×C₁₃	#3488	1	1	yes	characteristic
706	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
707	C₂×C₁₃	#3585	1	1	yes	characteristic
708	C₂⁴	—	2	1	no	—
709	C₂⁴	—	2	4	no	—
710	C₂⁴	—	2	2	no	—
711	#41	—	2	4	no	—
712	#41	—	2	4	no	—
713	#41	—	4	2	no	—
714	#41	—	4	8	no	—
715	#41	—	4	8	no	—
716	#41	—	4	4	no	—
717	C₂×Q₈	—	2	1	no	—
718	C₂×Q₈	—	2	1	no	—
719	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	4	1	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	4	8	no	—
743	C₂×D₄	—	4	16	no	—
744	C₂×D₄	—	4	8	no	—
745	C₂×D₄	—	4	4	no	—
746	C₂×D₄	—	8	2	no	—
747	C₂×D₄	—	8	4	no	—
748	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
749	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
751	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	4	4	no	—
764	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
765	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
770	SD₁₆	—	4	4	no	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	D₈	—	2	8	no	—
774	D₈	—	2	4	no	—
775	D₈	—	4	4	no	—
776	D₈	—	4	2	no	—
777	M₁₆	—	4	4	no	—
778	C₂×C₈	—	4	2	no	—
779	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
780	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
781	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
794	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
795	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
796	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
797	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	1	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
817	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
818	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	C₂×D₄×C₁₃	1	2	yes	—
823	C₄²	C₂×D₄×C₁₃	1	2	yes	—
824	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
825	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
826	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
827	C₄²	C₂⁴×C₁₃	1	2	yes	—
828	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
829	C₁₃	#61959	1	1	yes	characteristic, direct product factor, Sylow
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	8	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	8	1	no	—
839	C₂³	—	8	2	no	—
840	C₂³	—	8	4	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	4	no	—
843	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
844	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	Q₈	—	2	2	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	2	no	—
849	Q₈	—	8	1	no	—
850	D₄	—	2	4	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	1	no	—
855	D₄	—	2	1	no	—
856	D₄	—	2	1	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	8	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	4	no	—
869	D₄	—	8	4	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	4	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	complemented
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	8	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
897	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
905	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
906	C₈	—	2	4	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	4	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	4	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	16	4	no	—
928	C₂²	—	16	8	no	—
929	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
930	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
943	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
944	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
945	C₄	C₁₃×#585	1	1	yes	characteristic
946	C₂	—	2	2	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	1	no	—
950	C₂	—	8	4	no	—
951	C₂	—	8	2	no	—
952	C₂	C₁₃×#3488	1	1	yes	characteristic
953	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
954	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3498	C₂	semidirect
2. C₁₃×#3475	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3366	C₂	semidirect
5. C₁₃×#3325	C₂	semidirect
6. C₁₃×#3310	C₂	semidirect
7. C₁₃×#3272	C₂	semidirect
8. C₁₃×#3264	C₂	semidirect
9. C₁₃×#3251	C₂	semidirect
10. C₁₃×#3246	C₂	semidirect
11. C₁₃×#3217	C₂	semidirect
12. C₁₃×#3208	C₂	semidirect
13. C₁₃×#3115	C₂	semidirect
14. C₁₃×#3100	C₂	semidirect
15. C₁₃×#3038	C₂	semidirect
16. C₂×C₁₃×#459	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂²×C₁₃×D₈	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#555	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
31. C₁₃×#546	C₂²	semidirect
35. D₄²×C₁₃	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
42. C₂×C₁₃×#127	C₂²	semidirect
44. C₁₃×#529	C₂²	semidirect
47. C₄×C₁₃×#41	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#492	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#482	C₂²	semidirect
55. C₁₃×#480	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#476	C₂²	semidirect
58. C₁₃×#475	C₂²	semidirect
59. C₁₃×#474	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
61. C₁₃×#469	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#465	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#460	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#459	C₂²	semidirect
71. C₁₃×#459	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#459	C₂²	semidirect
74. C₁₃×#459	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#459	C₂²	semidirect
77. C₁₃×#450	C₂²	semidirect
78. C₁₃×#450	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
80. C₁₃×#447	C₂²	semidirect
81. C₁₃×#447	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₁₃×#442	C₂²	semidirect
84. C₁₃×#440	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
86. C₄×C₁₃×D₈	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
88. C₁₃×#435	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#431	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
93. C₁₃×#418	C₂²	semidirect
94. C₂×C₁₃×#102	C₂²	semidirect
231. #61959	C₁₃	direct (N × H)
353. #3498	C₂×C₁₃	semidirect
354. #3475	C₂×C₁₃	semidirect
355. #3397	C₂×C₁₃	semidirect
356. #3366	C₂×C₁₃	semidirect
357. #3325	C₂×C₁₃	semidirect
358. #3310	C₂×C₁₃	semidirect
359. #3272	C₂×C₁₃	semidirect
360. #3264	C₂×C₁₃	semidirect
361. #3251	C₂×C₁₃	semidirect
362. #3246	C₂×C₁₃	semidirect
363. #3217	C₂×C₁₃	semidirect
364. #3208	C₂×C₁₃	semidirect
365. #3115	C₂×C₁₃	semidirect
366. #3100	C₂×C₁₃	semidirect
367. #3038	C₂×C₁₃	semidirect
368. C₂×#459	C₂×C₁₃	semidirect
369. #2989	C₂×C₁₃	semidirect
414. D₄×C₁₃	H(5,𝔽₂)	semidirect
436. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
450. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
451. C₂²×D₈	C₂²×C₁₃	semidirect
452. #556	C₂²×C₁₃	semidirect
453. #555	C₂²×C₁₃	semidirect
454. #554	C₂²×C₁₃	semidirect
457. #552	C₂²×C₁₃	semidirect
460. #550	C₂²×C₁₃	semidirect
461. #547	C₂²×C₁₃	semidirect
462. #546	C₂²×C₁₃	semidirect
466. D₄²	C₂²×C₁₃	semidirect
469. #533	C₂²×C₁₃	semidirect
471. #532	C₂²×C₁₃	semidirect
473. C₂×#127	C₂²×C₁₃	semidirect
475. #529	C₂²×C₁₃	semidirect
478. C₄×#41	C₂²×C₁₃	semidirect
479. C₂×C₄×D₄	C₂²×C₁₃	semidirect
481. #496	C₂²×C₁₃	semidirect
482. #492	C₂²×C₁₃	semidirect
483. #490	C₂²×C₁₃	semidirect
484. #486	C₂²×C₁₃	semidirect
485. #482	C₂²×C₁₃	semidirect
486. #480	C₂²×C₁₃	semidirect
487. #478	C₂²×C₁₃	semidirect
488. #476	C₂²×C₁₃	semidirect
489. #475	C₂²×C₁₃	semidirect
490. #474	C₂²×C₁₃	semidirect
491. #474	C₂²×C₁₃	semidirect
492. #469	C₂²×C₁₃	semidirect
493. #468	C₂²×C₁₃	semidirect
494. #465	C₂²×C₁₃	semidirect
495. #463	C₂²×C₁₃	semidirect
496. #461	C₂²×C₁₃	semidirect
497. #460	C₂²×C₁₃	semidirect
498. #460	C₂²×C₁₃	semidirect
499. #460	C₂²×C₁₃	semidirect
500. #460	C₂²×C₁₃	semidirect
501. #459	C₂²×C₁₃	semidirect
502. #459	C₂²×C₁₃	semidirect
503. #459	C₂²×C₁₃	semidirect
504. #459	C₂²×C₁₃	semidirect
505. #459	C₂²×C₁₃	semidirect
506. #459	C₂²×C₁₃	semidirect
507. #459	C₂²×C₁₃	semidirect
508. #450	C₂²×C₁₃	semidirect
509. #450	C₂²×C₁₃	semidirect
510. #449	C₂²×C₁₃	semidirect
511. #447	C₂²×C₁₃	semidirect
512. #447	C₂²×C₁₃	semidirect
513. #446	C₂²×C₁₃	semidirect
514. #442	C₂²×C₁₃	semidirect
515. #440	C₂²×C₁₃	semidirect
516. C₄×D₈	C₂²×C₁₃	semidirect
517. C₄×D₈	C₂²×C₁₃	semidirect
518. #436	C₂²×C₁₃	semidirect
519. #435	C₂²×C₁₃	semidirect
520. #432	C₂²×C₁₃	semidirect
521. #431	C₂²×C₁₃	semidirect
522. #423	C₂²×C₁₃	semidirect
523. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
524. #418	C₂²×C₁₃	semidirect
525. C₂×#102	C₂²×C₁₃	semidirect
829. C₁₃	#61959	direct (N × H)
874. D₄	C₁₃×H(5,𝔽₂)	semidirect
896. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3498	2
C₁₃×#3475	2
C₁₃×#3397	2
C₁₃×#3366	2
C₁₃×#3325	2
C₁₃×#3310	2
C₁₃×#3272	2
C₁₃×#3264	2
C₁₃×#3251	2
C₁₃×#3246	2
C₁₃×#3217	2
C₁₃×#3208	2
C₁₃×#3115	2
C₁₃×#3100	2
C₁₃×#3038	2
C₂×C₁₃×#459	2
C₁₃×#2989	2
#61959	13

Subgroups — C13×#61959 #15748298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61959 #15748298